In recent years, several unsupervised, "contrastive" learning algorithms in vision have been shown to learn representations that perform remarkably well on transfer tasks. We show that this family of algorithms maximizes a lower bound on the mutual information between two or more "views" of an image where typical views come from a composition of image augmentations. Our bound generalizes the InfoNCE objective to support negative sampling from a restricted region of "difficult" contrasts. We find that the choice of negative samples and views are critical to the success of these algorithms. Reformulating previous learning objectives in terms of mutual information also simplifies and stabilizes them. In practice, our new objectives yield representations that outperform those learned with previous approaches for transfer to classification, bounding box detection, instance segmentation, and keypoint detection. % experiments show that choosing more difficult negative samples results in a stronger representation, outperforming those learned with IR, LA, and CMC in classification, bounding box detection, instance segmentation, and keypoint detection. The mutual information framework provides a unifying comparison of approaches to contrastive learning and uncovers the choices that impact representation learning.